Water exchange rate - Aquaculture Engineering

The water exchange rate indicates how quickly the water in closed units is exchanged.

Water exchange rate

The water exchange rate indicates
how quickly the water in closed units is exchanged. This can be defined as the
period for which a specific water mole-cule stays in the unit before leaving
via the outlet (Fig. 13.3). As the new incoming water will be mixed with the
‘old’ water in the tank, the outlet water will always contain both new and old
water. It is important to realize this, and means that if one tank volume is
run into a tank full of old water, only part of the old water is exchanged, not
all. To describe this, the term ideal water exchange is used. When expecting
ideal water exchange and adding 1 l of new water to 100 l of old water, the new
and old water will be mixed immediately; for example, the addition of 1 l red
water to 100 l of clear water instantly results in pink water. This is a
simplification, but it helps us to understand better what is happening with the
water exchange, and does not require difficult equations.

Mathematically, the water
exchange rate can be calculated as follows (based on developing a differential
equation):

F =(1−e−t/th)×100

where:

t =time after start of filling water
into the unitth= time necessary to fill one tank
volume at the actual water flow rate; also known as the the-oretical retention
time

1.F = water exchange rate (proportion
of the water volume in the unit that is exchanged after time t)

Example

Fifty litres of new water is added to a tank that con-tains 100
l water, described as old water, over a period of 5 minutes (i.e. 10 l/min).
The same amount of old water flows out through the outlet because the water
volume and level are constant. How much of the water volume is exchanged after
5 and 10 min, respectively?

Setting t = 5 min

th= 100 l/(10 l/min) = 10 min

= (1 − e−5/10) × 100

= (1 – 0.605) × 100

=39.5%

Setting t = 10 min

F =63.2%

This means that by adding a water volume equal to the tank
volume only 63.2% of the water is exchanged, not all as might be expected, the
reason being that new and old water are mixed.